Question

How do you solve `\frac { 1} { 2} b - 9= 4b + 5`?

Answer 1

`b=-4`

Explanation:

To solve this equation, you need to isolate all of the terms with `b` on one side (usually the left) and isolate all of the terms without `b` on the other (usually the right):

`1/2b-9 = 4b+5`

Adding 9 to both sides:

`1/2b-9+9=4b+5+9`
`1/2b=4b+14`

To make things easier for us later, we can multiply both sides by 2 to get rid of the `1/2`:

`2(1/2b)=2(4b+14)`
`b=2(4b)+2(14)`
`b=8b+28`

Subtracting `8b` from both sides:

`b-8b=8b-8b+28`
`-7b=28`

Dividing both sides by `-7`:

`{-7b}/{-7}=28/{-7}`
`b=-4`

To check our work, we can plug in -4 for b and test the equality:

`1/2(-4)-9 = 4(-4)+5`
`-2-9=-16+5`
`-11=-11`

Since this equality works out, we did everything right.

Answer 2

See explanation

Explanation:

`1/2b = 4b + 14 rarr` Add 9 to each side

`b = 8b + 28 rarr` Multiply each side by 2 to get rid of the fraction

`-7b = 28 rarr` Subtract 8b from each side

`b = -4 rarr` Divide each side by -7